Finite Group DatabasebetaFinite Group Databasebeta| order | 14864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16836500 |
| unambiguous semidirect product | (C2×#16836500)⋊C2 |
| Fitting | C22×C929 ⋊ C4 |
| Sylow | C929 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3716 |
Polycyclic presentation:
2^4,929|a^2=d,b^a=bc,e^a=e^605,e^d=e^928938 conjugacy classes — view the full character table.
| maximal subgroup of | #44446432, #44446433, C2×C22⋊#16836500, … |
| maximal normal subgroup of | #44446432, #44446433, C2×C22⋊#16836500, … |
| maximal quotient of | (C2×#16836500)⋊C4, C22⋊#21418259, #44446431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14864, 45);